Statistical microdamage mechanics and damage field evolution

Discussed are the underlying background of statistical microdamage mechanics, the fundamental partial differential equation of evolution of microdamage number density, two basic solutions, and the saturation of microdamage number density evolution. Knowledge of microdamage number density evolution is applied to engineering practice by using the field equations of microdamage number density and continuum damage. The addition of continuum equations renders a complete system of field equations of deformation and damage. However, they are open-ended in character at the continuum level although the dynamic damage function is completed from the meso- to the macro-scale level. Once decoupling of the function is made, the system of equations can be connected in an approximate manner. This provides a reasonable approximation to the continuum field of deformation and damage. The open literature prediction based on damage evolution relies on assuming arbitrary critical damage states. In this work, use is made of the criterion for damage localization. Several applications of statistical microdamage mechanics are made. This includes damage evolution in a heterogeneous medium and failure forecast under impact. The results show that statistical microdamage mechanics and the derived closed approximate continuum formulations are physically sound and practically effective

Coupling effects of heterogeneity and stress fluctuation on rupture

The coupling of mesoscopic strength distribution and stress fluctuation on damage evolution and rupture are examined. The numerical simulations show that there is only weak stress fluctuation at the initial damage stage when the mean field approximation is in effect. As the damage fraction becomes larger than the threshold value, the fluctuation is amplified significantly, and damage localization appears. The coupling between stress fluctuation, disordered heterogeneity and the damage localization may play an essential role in catastrophic rupture. (C) 2003 Elsevier Ltd. All rights reserved